Novel Estimations of Hadamard-Type Integral Inequalities for Raina’s Fractional Operators

Abstract

In the present paper, utilizing a wide class of fractional integral operators (namely the Raina fractional operator), we develop novel fractional integral inequalities of the Hermite–Hadamard type. With the help of the well-known Riemann–Liouville fractional operators, s-type convex functions are derived using the important results. We also note that some of the conclusions of this study are more reasonable than those found under certain specific conditions, e.g., s=1, λ=α, σ(0)=1, and w=0. In conclusion, the methodology described in this article is expected to stimulate further research in this area.

Keywords

• Raina fractional operator
• s-type convex function
• Jensen inequality
• Hermite–Hadamard inequality
• Hölder inequality
• young inequality